Optical fibers are used for a variety of applications where light needs to be delivered from a light source to a remote location. Optical telecommunication systems, for example, rely on a network of optical fibers to transmit light from a service provider to system end-users.
Optical fibers are typically designed to efficiently deliver light from one end of the fiber to the other end of the fiber (usually over long distances), which requires that very little light escapes from the sides of the typical fiber. Yet, there are a number of applications such as special lighting, signage, or biological applications, including bacteria growth and the production of photo-bioenergy and biomass fuels, where select amounts of light need to be provided in an efficient manner to the specified areas.
To this end, light-diffusing optical fibers have been developed, such as described in U.S. Pat. No. 7,450,806, and U.S. Pre-Grant Publications US2012/0275180, US2011/0122646, and US2013/0107565. Light-diffusing optical fibers are configured to scatter light out of the fiber along the length of the fiber. Light-diffusing fibers are used in a variety of applications, such as light sources (see, e.g., WO 2013/055842 A1).
Light diffusing optical fibers can be optically coupled to a laser-diode light source with a coupling efficiency of greater than 90% due to the small and relative low numerical aperture (NA) of laser diodes. However, for certain applications, it is preferred to use light-emitting diodes (LEDs) as the light source. The coupling of an LED to a light-diffusing optical fiber is challenging because the core of a light-diffusing fiber can have a diameter that ranges from 125 μm to 250 μm and has a NA of about 0.35, while an LED has a size of about 1 mm or larger and a large NA, e.g., from about 0.86 and up to about 1.
In an optical system, the etendue is conserved. In geometric terms relating to a light source and an optical fiber, if A1 and A2 are respectively the size of a light source emitting area and the fiber core, and NA1 and NA2 are respectively the source and fiber numerical apertures, then A1·(NA1)2=A2·(NA2)2. Consequently, the optical coupling between a light-diffusing optical fiber and an LED light source would be unacceptably low due to the mismatch between numerical apertures and emitting/receiving areas.